Complex mexican hat wavelet
- Complex mexican hat wavelet
-
The complex Mexican hat wavelet is a low-oscillation, complex-valued, wavelet for the continuous wavelet transform. This wavelet is formulated in terms of its Fourier transform as the Hilbert analytic function of the conventional Mexican hat wavelet:
Temporally, this wavelet can be expressed in terms of the error function, as:
This wavelet has O( | t | − 3) asymptotic temporal decay in | Ψ(t) | , dominated by the discontinuity of the second derivative of at ω = 0.
This wavelet was proposed in 2002 by Addison et al. for applications requiring high temporal precision time-frequency analysis.
References
1. Paul S. Addison Wavelet Page - Low-Oscillation Complex Wavelets, P. S. Addison, et al., The Journal of Sound and Vibration, 2002
Wikimedia Foundation.
2010.
Look at other dictionaries:
Wavelet — A wavelet is a mathematical function used to divide a given function or continuous time signal into different frequency components and study each component with a resolution that matches its scale. A wavelet transform is the representation of a… … Wikipedia
Continuous wavelet — In numerical analysis, continuous wavelets are functions used by the continuous wavelet transform. These functions are defined as analytical expressions, as functions either of time or of frequency. Most of the continuous wavelets are used for… … Wikipedia
List of functional analysis topics — This is a list of functional analysis topics, by Wikipedia page. Contents 1 Hilbert space 2 Functional analysis, classic results 3 Operator theory 4 Banach space examples … Wikipedia
List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… … Wikipedia
List of mathematics articles (M) — NOTOC M M estimator M group M matrix M separation M set M. C. Escher s legacy M. Riesz extension theorem M/M/1 model Maass wave form Mac Lane s planarity criterion Macaulay brackets Macbeath surface MacCormack method Macdonald polynomial Machin… … Wikipedia